Stability in gauged extended supergravity

We study a subsector of the AdS 4 /CFT 3 correspondence where a class of solutions in the bulk and on the boundary can be explicitly compared. The bulk gravitational theory contains a conformally coupled scalar field with a φ 4 potential, and is holographically related to a massless scalar with a φ 6 interaction in three dimensions. We consider the scalar sector of the bulk theory and match bulk and boundary classical solutions of the equations of motion. Of particular interest is the matching of the bulk and the boundary instanton solutions which underlies the relationship between bulk and boundary vacua with broken conformal invariance. Using a form of radial quantization we show that quantum states in the bulk correspond to multiply-occupied single particle quantum states in the boundary theory. This allows us to explicitly identify the boundary composite operator which is dual to the bulk scalar, at the free theory level as well as in the instanton vacuum. We conclude with a discussion of possible implications of our results.

Section: Classical Correspondencesupporting

confidence: 75%

Instantons and conformal holography

Haro

Petkou

2006

“…The scalar potential of 5-d gauged supergravity has several stationary points. All stationary points that satisfy the Breitenlohner-Freedman stability bound [16] correspond to local, unitary, four-dimensional conformal field theories. Some of these stationary points have been studied in [17,18,19].…”

Section: General Resultsmentioning

confidence: 99%

Confinement and condensates without fine tuning in supergravity duals of gauge theories

Girardello

Petrini

Porrati

et al. 1999

103

159

Abstract:We discuss a solution of the equations of motion of five-dimensional gauged type IIB supergravity that describes confining SU(N) gauge theories at large N and large 't Hooft parameter. We prove confinement by computing the Wilson loop, and we show that our solution is generic, independent of most of the details of the theory. In particular, the Einstein-frame metric near its singularity, and a contribution to the condensates of scalar, composite operators are universal. Also universal is the discreteness of the glueball mass spectrum and the existence of a mass gap. The metric is also identical to a generically confining solution recently found in type 0B theory.

“…Likewise, we note that the form of (2.7) remains invariant under 14) under which its parameters transform as a → a − 1, δ → δ ∓ 1 .…”

Section: Scalar Fieldsmentioning

confidence: 89%

“…The fluctuation equations for χ and c decouple from the others and after some computation give rise to 14) for the combinations…”

Section: Scalar Sphere Harmonicsmentioning

confidence: 99%

Supergravity Duals of Matrix String Theory

Morales¹,

Samtleben²

2002

We study holographic duals of type II and heterotic matrix string theories described by warped AdS 3 supergravities. By explicitly solving the linearized equations of motion around near horizon D-string geometries, we determine the spectrum of Kaluza-Klein primaries for type I, II supergravities on warped AdS 3 × S 7 . The results match those coming from the dual two-dimensional gauge theories living on the D-string worldvolumes. We briefly discuss the connections with the N = (8, 8), N = (8, 0) orbifold superconformal field theories to which type IIB/heterotic matrix strings flow in the infrared. In particular, we associate the dimension (h,h) = ( 3 2 , 3 2 ) twisted operator which brings the matrix string theories out from the conformal point (R 8 ) N /S N with the dilaton profile in the supergravity background.The familiar dictionary between masses and "scaling" dimensions of field and operators are modified by the presence of non-trivial warp factors and running dilatons. These modifications are worked out for the general case of domain wall/QFT correspondences between supergravities on warped AdS d+1 × S q geometries and super Yang-Mills theories with 16 supercharges.